there is no policy for pets, but they have cats?

The Fair Housing Amendments of 1988, Section 504 of the Rehabilitation Act of 1973 and Title II of the Americans with Disabilities Act protect the rights of persons with disabilities to keep emotional support animals, even when an owner's policy explicitly prohibits pets. Because emotional support and assistance animals are not "pets", but is considered more than technical aids such as wheelchairs, the law generally requires the owner to make an exception to a "no pets" policy to the tenant with a disability can fully use and enjoy housing. In most housing complexes, the tenant has a letter or a prescription from a competent professional as a therapist or doctor, and meets the definition of a person with a disability, he or she is entitled to reasonable accommodations that allow for emotional support animals between apartment.Some people may also be allowed to bring pets in a restaurant …..

What is the question? Yes, if the cat is an ESA may be in a home with no pets policy. No person shall bring a pet in a restaurant. Only service dogs (for the sake of change) are allowed in restaurants and service dogs are not pets.